New Results on the Thermodynamic Properties of the Climate System

Abstract

In this paper the authors exploit two equivalent formulations of the average rate of material entropy production in the climate system to propose an approximate splitting between contributions due to vertical and eminently horizontal processes. This approach is based only on 2 D radiative fields at the surface and at the top of atmosphere. Using 2D fields at the top of atmosphere alone, lower bounds to the rate of material entropy production and to the intensity of the Lorenz energy cycle are derived. By introducing a measure of the efficiency of the planetary system with respect to horizontal thermodynamic processes, it is possible to gain insight into a previous intuition on the possibility of defining a baroclinic heat engine extracting work from the meridional heat flux. The approximate formula of the material entropy production is verified and used for studying the global thermodynamic properties of climate models (CMs) included in the Program for Climate Model Diagnosis and Intercomparison (PCMDI)/phase 3 of the Coupled Model Intercomparison Project (CMIP3) dataset in preindustrial climate conditions. It is found that about 90% of the material entropy production is due to vertical processes such as convection, whereas the large-scale meridional heat transport contributes to only about 10% of the total. This suggests that the traditional two-box models used for providing a minimal representation of entropy production in planetary systems are not appropriate, whereas a basic but conceptually correct description can be framed in terms of a four-box model. The total material entropy production is typically 55 mW m(-2) K(-1), with discrepancies on the order of 5%, and CMs' baroclinic efficiencies are clustered around 0.055. The lower bounds on the intensity of the Lorenz energy cycle featured by CMs are found to be around 1.0-1.5 W m(-2), which implies that the derived inequality is rather stringent. When looking at the variability and covariability of the considered thermodynamic quantities, the agreement among CMs is worse, suggesting that the description of feedbacks is more uncertain. The contributions to material entropy production from vertical and horizontal processes are positively correlated, so that no compensation mechanism seems in place. Quite consistently among CMs, the variability of the efficiency of the system is a better proxy for variability of the entropy production due to horizontal processes than that of the large-scale heat flux. The possibility of providing constraints on the 3D dynamics of the fluid envelope based only on 2D observations of radiative fluxes seems promising for the observational study of planets and for testing numerical models

Vertical and horizontal processes in the global atmosphere and the maximum entropy production conjecture

“…Finally in Sect. 4.1 we analyse the solutions in terms of vertical/horizontal splitting and provide some new independent estimates which agree with results in Lucarini et al (2011).…”

“…A very similar formula has also been derived from first principles by Lucarini et al (2011).Ṡ mat is therefore the sum of two …”

“…Such a model is not meant to be a more involved version of the two-box model described by Lorenz et al (2001) but rather a minimal conceptual model for material entropy production in a planetary system, as proposed by Lucarini et al (2011), since it accounts for both horizontal and vertical transport processes. Lucarini et al (2011) claim that two-box models as in Lorenz et al (2001), by neglecting vertical processes, do not provide a realistic description of the material entropy production and therefore cannot be used to test MEP. The longwave and shortwave transmissivities of each atmospheric box, τ l,i , τ s,i , i = 1, 2 are prescribed and to be considered parameters of the model.…”

“…In the real climateṠ ver can be thought of as the entropy production due to the sum of latent and sensible heat fluxes at the surface (Kleidon, 2009) and, to a minor extent, turbulent dissipation of kinetic energy. Lucarini et al (2011) have shown thatṠ hor is a lower bound of entropy production due to dissipation of kinetic energy. Material entropy production is therefore a function of (M, H 1 , H 2 ) and thus defined in the (M, H 1 , H 2 ) space.…”

“…The total material entropy production of the climate system has been estimated from general circulation models to be about 50 mW K −1 m −2 and most of it is associated with the hydrological cycle whereas only a small (10 %) fraction is associated with large scale meridional heat transport (Ambaum, 2010;Fraedrich and Lunkeit, 2008;Pascale et al, 2011a). On the basis of this, recently Lucarini et al (2011) have questioned the appropriateness of 2-box models as the paradigmatic one used by Lorenz et al (2001) as a tool to investigate MEP. Given the large difference in the magnitude of the two contributions as well as the different nature of the atmospheric motions (fast small-scale vertical processes such as convection vs. slower large scale meridional heat transport) from which they are generated, substantial difference may be expected when considering MEP.…”